Functional Approach to Optimal Experimental Design

Author: Viatcheslav B. Melas
Publisher: Springer Science & Business Media
ISBN: 0387316108
Format: PDF, ePub, Mobi
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The present book is devoted to studying optimal experimental designs for a wide class of linear and nonlinear regression models. This class includes polynomial, trigonometrical, rational, and exponential models as well as many particular models used in ecology and microbiology. As the criteria of optimality, the well known D-, E-, and c-criteria are implemented. The main idea of the book is to study the dependence of optimal - signs on values of unknown parameters and on the bounds of the design interval. Such a study can be performed on the base of the Implicit Fu- tion Theorem, the classical result of functional analysis. The idea was ?rst introduced in the author’s paper (Melas, 1978) for nonlinear in parameters exponential models. Recently, it was developed for other models in a n- ber of works (Melas (1995, 2000, 2001, 2004, 2005), Dette, Melas (2002, 2003), Dette, Melas, Pepelyshev (2002, 2003, 2004b), and Dette, Melas, Biederman (2002)). Thepurposeofthepresentbookistobringtogethertheresultsobtained and to develop further underlying concepts and tools. The approach, m- tioned above, will be called the functional approach. Its brief description can be found in the Introduction. The book contains eight chapters. The ?rst chapter introduces basic concepts and results of optimal design theory, initiated mainly by J.Kiefer.

Optimal Experimental Design with R

Author: Dieter Rasch
Publisher: CRC Press
ISBN: 1439816980
Format: PDF, ePub, Docs
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Experimental design is often overlooked in the literature of applied and mathematical statistics: statistics is taught and understood as merely a collection of methods for analyzing data. Consequently, experimenters seldom think about optimal design, including prerequisites such as the necessary sample size needed for a precise answer for an experimental question. Providing a concise introduction to experimental design theory, Optimal Experimental Design with R: Introduces the philosophy of experimental design Provides an easy process for constructing experimental designs and calculating necessary sample size using R programs Teaches by example using a custom made R program package: OPDOE Consisting of detailed, data-rich examples, this book introduces experimenters to the philosophy of experimentation, experimental design, and data collection. It gives researchers and statisticians guidance in the construction of optimum experimental designs using R programs, including sample size calculations, hypothesis testing, and confidence estimation. A final chapter of in-depth theoretical details is included for interested mathematical statisticians.

Optimum Experimental Designs With SAS

Author: Anthony Atkinson
Publisher: Oxford University Press
ISBN: 0199296596
Format: PDF, ePub, Docs
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Experiments in the field and in the laboratory cannot avoid random error and statistical methods are essential for their efficient design and analysis. Authored by leading experts in key fields, this text provides many examples of SAS code, results, plots and tables, along with a fully supported website.

mODa 8 Advances in Model Oriented Design and Analysis

Author: Jesus Lopez-Fidalgo
Publisher: Springer Science & Business Media
ISBN: 3790819522
Format: PDF, Kindle
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This volume contains the proceedings of the 8th Workshop on Model-Oriented Design and Analysis. It offers leading and pioneering work on optimal experimental designs, both from a mathematical/statistical point of view and with regard to real applications. Scientists from all over the world have contributed to this volume. Primary topics are designs for nonlinear models and applications to experimental medicine.

Optimal Design for Nonlinear Response Models

Author: Valerii V. Fedorov
Publisher: CRC Press
ISBN: 1439821518
Format: PDF, ePub
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Optimal Design for Nonlinear Response Models discusses the theory and applications of model-based experimental design with a strong emphasis on biopharmaceutical studies. The book draws on the authors’ many years of experience in academia and the pharmaceutical industry. While the focus is on nonlinear models, the book begins with an explanation of the key ideas, using linear models as examples. Applying the linearization in the parameter space, it then covers nonlinear models and locally optimal designs as well as minimax, optimal on average, and Bayesian designs. The authors also discuss adaptive designs, focusing on procedures with non-informative stopping. The common goals of experimental design—such as reducing costs, supporting efficient decision making, and gaining maximum information under various constraints—are often the same across diverse applied areas. Ethical and regulatory aspects play a much more prominent role in biological, medical, and pharmaceutical research. The authors address all of these issues through many examples in the book.

Robust Planning and Analysis of Experiments

Author: Christine H. Mueller
Publisher: Springer Science & Business Media
ISBN: 1461222966
Format: PDF, Mobi
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Robust statistics and the design of experiments are two of the fastest growing fields in contemporary statistics. Up to now, there has been very little overlap between these fields. This is the first book to link these two areas by studying the influence of the design on the efficiency and robustness of robust estimators and tests. The classical approaches of experimental design and robust statistics are introduced before the areas are linked, and the author shows that robust statistical procedures profit by an appropriate choice of the design and that efficient designs for a robust statistical analysis are more applicable.